Sammanfattning: Development of silicon based electronics have revolutionized our every day life during the last five decades. Nowadays silicon based devices operate close to their theoretical limits that is becoming a bottleneck for further progress. In particular, for the growing field of high frequency and high power electronics, silicon cannot offer the required properties. Development of materials capable of providing high current densities, carrier mobilities and high breakdown fields is crucial for further progress in state of the art electronics.Epitaxial graphene grown on semi-insulating silicon carbide substrates has a high potential to be integrated in current planar device technologies. High electron mobilities and sheet carrier densities make graphene extremely attractive for high frequency analog applications. One of the remaining challenges is the interaction of epitaxial graphene with the substrate. Typically, much lower free charge carrier mobilities, compared to free standing graphene, and doping, due to charge transfer from the substrate, is reported. Thus, a good understanding of the intrinsic free charge carriers properties and the factors affecting them is very important for further development of epitaxial graphene.Group III-nitrides have been extensively studied and already have proven their high efficiency as light emitting diodes for short wavelengths. High carrier mobilities and breakdown electric fields were demonstrated for group III-nitrides, making them attractive for high frequency and high power applications. Currently, In-rich InGaN alloys and AlGaN/GaN high electron mobility structures are of high interest for the research community due to open fundamental questions such as free charge carrier properties at high temperatures and wavefunction hybridization in AlGaN/GaN heterostructures.Electrical characterization techniques, commonly used for the determination of free charge carrier properties, require good ohmic and Schottky contacts, which in certain cases can be difficult to achieve. Access to electrical properties of buried conductive channels in multilayered structures requires modification of samples and good knowledge of the electrical properties of all electrical junctions within the structure. Moreover, the use of contacts to electrically characterize two-dimensional electronic materials, such as graphene, can alter their intrinsic properties. Furthermore, the determination of effective mass parameters commonly employs cyclotron resonance and Shubnikov-de Haas oscillations measurements, which require long scattering times of free charge carriers, high magnetic fields and low temperatures.The optical Hall effect is an external magnetic-field induced birefringence of conductive layers due to the free charge carriers interaction with long-wavelength electromagnetic waves under the influence of the Lorentz force. The optical Hall effect can be measured by generalized ellipsometry and provides a powerful method for the determination of free charge carrier properties in a non-destructive and contactless manner. The optical Hall effect measurements can provide quantitative information about free charge carrier type, concentration, mobility and effective mass parameters at temperatures ranging from few kelvins to room temperature and above. It further allows to differentiate the free charge carrier properties of individual layers in multilayer samples. The employment of a backside cavity for transparent samples can enhance the optical Hall effect and allows to access free charge carrier properties at relatively low magnetic fields using permanent magnet.The optical Hall effect measurements at mid-infrared spectral range can be used to probe quantum mechanical phenomena such as Landau levels in graphene. The magnetic field dependence of the inter-Landau level transition energies and optical polarization selection rules provide information about coupling properties between graphene layers and the electronic band structure.Measurement of the optical Hall effect by generalized ellipsometry is an indirect technique requiring subsequent data analysis. Parameterized optical models are fitted to match experimentally measured ellipsometric spectra by varying physically significant model parameters. Analysis of the generalized ellipsometry data at long wavelengths for samples containing free charge carriers by optical models based on the classical Drude formulation, augmented with an external magnetic field contribution, allows to extract carrier concentration, mobility and effective mass parameters.The development of the integrated FIR and THz frequency-domain ellipsometer at the Terahertz Materials Analysis Center in Linköping University was part of the graduate studies presented in this dissertation. The THz ellipsometer capabilities are demonstrated by determination of Si and sapphire optical constants, and free charge carrier properties of two-dimensional electron gas in GaN-based high electron mobility transistor structures. The THz ellipsometry is further shown to be capable of determining free charge carrier properties and following their changes upon variation of ambient conditions in atomically thin layers with an example of epitaxial graphene.A potential of the THz OHE with the cavity enhancement (THz-CE-OHE) for determination of the free charge carrier properties in atomically thin layers were demonstrated by the measurements of the carrier properties in monolayer and multilayer epitaxial graphene on Si-face 4H-SiC. The data analysis revealed p-type doping for monolayer graphene with a carrier density in the low 1012 cm-2 range and a carrier mobility of 1550 cm2V-1s-1. For the multilayer graphene, n-type doping with a carrier density in the low 1013 cm-2 range, a mobility of 470 cm2V-1s-1 and an effective mass of (0.14 ± 0.03)m0 were extracted. Different type of doping among monolayer and multilayer graphene is explained as a result of different hydrophobicity among samples.Further, we have employed THz-CE-OHE to determine for the first time anisotropic mobility parameter in quasi-free-standing bilayer epitaxial graphene induced by step-like surface morphology of 4H-SiC. Correlation of atomic force microscopy, Raman scattering spectroscopy, scanning probe Kelvin probe microscopy, low energy electron microscopy and diffraction analysis allows us to investigate the possible scattering mechanisms and suggests that anisotropic mobility is induced by varying local mobility parameter due to interaction between graphene and underlaying substrate.The origin of the layers decoupling in multilayer graphene on C-face 4H-SiC was studied by MIR-OHE, transmission electron microscopy and electron energy loss spectroscopy. The results revealed the decoupling of the layers induced by the increased interlayer spacing which is attributed to the Si atoms trapped between graphene layers.MIR ellipsometry and MIR-OHE measurements were employed to determine the electron effective mass in a wurtzite In0.33Ga0.67N epitaxial layer. The data analysis revealed the effective mass parameters parallel and perpendicular to the c-axis which can be considered as equal within sensitivity of our measurements. The determined effective mass is consistent with linear dependence on the In content.Analysis of the free charge carrier properties in AlGaN/GaN high electron mobility structures with modified interfaces showed that AlGaN/GaN interface structure has a significant effect on the mobility parameter. A sample with a sharp interface layers exhibits a record mobility of 2332 ± 73 cm2V-1s-1. The determined effective mass parameters showed an increase compared to the bulk GaN value, which is attributed to the penetration of the electron wavefunction into the AlGaN barrier layer.Temperature dependence of free charge carrier properties in GaN-based high electron mobility transistor structures with AlGaN and InAlN barrier layers were measured by terahertz optical Hall effect technique in a temperature range from 7.2 K to 398 K. The results revealed strong changes in the effective mass and mobility parameters. At temperatures below 57 K very high carrier mobility parameters above 20000 cm2V-1s-1 for AlGaN-barrier sample and much lower mobilities of ~ 5000 cm2V-1s-1 for InAlN-barrier sample were obtained. At low temperatures the effective mass parameters for both samples are very similar to bulk GaN value, while at temperatures above 131 K effective mass shows a strong increase with temperature. The effective masses of 0.344 m0 (@370 K) and 0.439 m0 (@398 K) were obtained for AlGaN- and InAlN-barrier samples, respectively. We discussed the possible origins of effective mass enhancement in high electron mobility transistor structures.